SOLUTION: Joy wants to buy carpet for a room that is 19 ft wide and 26 ft. long. She wants to leave a uniform strip of flooring around the carpet. She can afford to purchase 198 sq. ft. of c

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Question 974949: Joy wants to buy carpet for a room that is 19 ft wide and 26 ft. long. She wants to leave a uniform strip of flooring around the carpet. She can afford to purchase 198 sq. ft. of carpet. What should the dimensions of the carpet be?
Found 2 solutions by Boreal, josgarithmetic:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
The carpet has to be (19-x)(26-x)-198 sq ft; x=feet of uniform flooring strip
494-45x+x^2=198
x^2-45x+296=0
(x-37)(x-8)=0
x=37,8; x=37 is not possible
x=8 feet of flooring ANSWER
check 11 *18=198 sq ft.

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
w, width of room
L, length of room
u, uniform width around carpet
A, area of carpet-
-
w=19
L=26
u, UNKNOWN
A=198
-
Finding u will allow for finding dimensions of the carpet

wL-A, the area of the uniform strip between walls and carpet
%28w-2u%29%28L-2u%29=A, the dimensions of the carpet arranged to express carpet's area A.

wL-2Lu-2wu%2B4u%5E2-A=0
4u%5E2-%282L%2B2w%29u%2BwL-A=0
4u%5E2-2%28L%2Bw%29u%2BwL-A=0
Doing the substitutions now might be much more comfortable...
4u%5E2-2%2826%2B19%29u%2B26%2A19-198=0
4u%5E2-90u%2B296=0
highlight_green%282u%5E2-45u%2B148=0%29
Try the general solution for a quadratic equation to solve for u.

u=%2845%2B-+sqrt%2845%5E2-4%2A2%2A148%29%29%2F4
u=%2845%2B-+sqrt%28841%29%29%2F4
u=%2845%2B-+29%29%2F4
highlight%28u=4%29 or cross%28u=18.5%29
Obviously only u=4 makes sense.

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Rug width, 11
Rug length, 18
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